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Updated on: 06 Jul 2025, 23:38
Originally posted by EgmatQuantExpert on 16 May 2018, 07:37.
Last edited by Bunuel on 06 Jul 2025, 23:38, edited 8 times in total.
Last edited by Bunuel on 06 Jul 2025, 23:38, edited 8 times in total.
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
50% (03:30) correct
50%
(03:12)
wrong
based on 193
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A bus made a roundtrip journey from Madison towards Chicago, which is 240 km away. In the onward journey the bus divided the journey time in 3 equal blocks. Started at 50 kph, it took stoppages after every block and increased its speed by 10 kph after every stoppage. At Chicago, it took a halt of 7 hrs 44 minutes. The return journey was divided into two equidistant blocks, covered at 45 kph and 75 kph respectively. Find by what amount the average speed of the whole journey of the bus is less than the sum of the average speeds of onward and return journey;
A. 75 kph
B. 86.25 kph
C. 97.5 kph
D. 105 kph
E. 120 kph
A. 75 kph
B. 86.25 kph
C. 97.5 kph
D. 105 kph
E. 120 kph
3 common mistakes you must avoid in Distance questions – Practice question 2
To solve question 3: Question 3
To read the article: 3 common mistakes you must avoid in Distance questions
To solve question 3: Question 3
To read the article: 3 common mistakes you must avoid in Distance questions
16 May 2018, 07:40
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Solution
Given:
• A bus made a roundtrip journey from Madison to Chicago
• Distance between Madison and Chicago = 240 km
• In the onward journey, the total journey time was divided into 3 equal blocks
• The bus increased its speed by 10 kph after every stoppage
- o Speed in the 1st time block = 50 kph
o Speed in the 2nd time block = 60 kph
o Speed in the 3rd (final) time block = 70 kph
• In the return journey, the total journey was divided into 2 equal distance blocks
- o Speed in the 1st distance block = 45 kph
o Speed in the 2nd distance block = 75 kph
To find:
• The value of the average speed of the bus in the whole journey is what amount less than the sum of the average speeds of the onward and return journeys
Approach and Working:
• In the onward journey, let us assume each time block takes t hrs
- o Therefore, we can say 50t + 60t + 70t = 240
Or, 180t = 240
Or, t = \(\frac{240}{180}\) hrs = \(\frac{4}{3}\) hrs
• Therefore, the average speed in the onward journey = \(\frac{240}{4}\) kph = 60 kph
[as the time taken in each block is same, we could have also calculated the average speed by taking the arithmetic mean of the individual speeds, i.e. \(\frac{(50 + 60 + 70)}{3}\) = 60 mph]
• In the return journey, because the total distance is equally divided into 2 parts, we can say the average speed is = \(\frac{(2 * 45 * 75)}{(45 + 75)}\) = 56.25 kph
• Also, the time taken in the return journey = (\(\frac{120}{45} + \frac{120}{75}\)) hrs = (\(\frac{8}{3} + \frac{8}{5}\)) hrs = \(\frac{64}{15}\) hrs
• Now, if we consider the whole journey,
The total time taken = (\(4 + \frac{116}{15} + \frac{64}{15}\)) hrs = 16 hrs
- o Total distance travelled = (240 + 240) km = 480 km
• So, the amount by which overall average speed is less than the sum of the individual average speeds = (60 + 56.25) – 30 kph = 116.25 – 30 kph = 86.25 kph
Hence, the correct answer is option B.
Answer: B
General Discussion
05 Mar 2020, 00:24
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EgmatQuantExpert
why do you assume the time take for the bus to travel each block is equal? It doesn't say that in the problem, just that the distances were equal.
first trip = 240/(80/50+80/60+80/70) = 58.87
2nd trip = 240/(120/45+120/75) = 56.25
Average of the whole trip 480/(80/50+80/60+80/70+120/45+120/75) = 57.53
58.87+56.25 - 57.53 =~ 59+56-58 = 57
